Quantum teleportation between remoteatomic-ensemble quantum memoriesXiao-Hui Baoa,b,c, Xiao-Fan Xuc, Che-Ming Lic,d, Zhen-Sheng Yuana,b,c, Chao-Yang Lua,b,1, and Jian-Wei Pana,b,c,1

aHefei National Laboratory for Physical Sciences at Microscale and bDepartment of Modern Physics, University of Science and Technology of China, Hefei,Anhui 230026, China; cPhysikalisches Institut der Universitaet Heidelberg, 69120 Heidelberg, Germany; and dDepartment of Engineering Science andSupercomputing Research Center, National Cheng Kung University, Tainan 701, Taiwan

Edited by Alain Aspect, Institut d’Optique, Orsay, France, and approved October 11, 2012 (received for review May 2, 2012)

Quantum teleportation and quantum memory are two crucialelements for large-scale quantum networks. With the help of priordistributed entanglement as a “quantum channel,” quantum tele-portation provides an intriguing means to faithfully transfer quan-tum states among distant locations without actual transmission ofthe physical carriers [Bennett CH, et al. (1993) Phys Rev Lett 70(13):1895–1899]. Quantum memory enables controlled storageand retrieval of fast-flying photonic quantum bits with stationarymatter systems, which is essential to achieve the scalability re-quired for large-scale quantum networks. Combining these twocapabilities, here we realize quantum teleportation between tworemote atomic-ensemble quantum memory nodes, each composedof ∼108 rubidium atoms and connected by a 150-m optical fiber.The spin wave state of one atomic ensemble is mapped to a prop-agating photon and subjected to Bell state measurements withanother single photon that is entangled with the spin wave stateof the other ensemble. Two-photon detection events herald thesuccess of teleportation with an average fidelity of 88(7)%. Be-sides its fundamental interest as a teleportation between two re-mote macroscopic objects, our technique may be useful forquantum information transfer between different nodes in quan-tum networks and distributed quantum computing.

cold atomic ensembles | long-distance quantum communication | quantumcomputation | light–matter interface

Single photons are so far the best messengers for quantumnetworks as they are naturally propagating quantum bits

(qubits) and have very weak coupling to the environment (1, 2).However, due to the inevitable photon loss in the transmissionchannel, the quantum communication is limited currently to adistance of about 200 km (3, 4). To achieve scalable long-distancequantum communication (5, 6), quantum memories are required(7–10), which coherently convert a qubit between light and matterefficiently on desired time points so that operations can be ap-propriately timed and synchronized. The connection of distantmatter qubit nodes and transfer of quantum information betweenthe nodes can be done by distributing atom–photon entanglementthrough optical channels and quantum teleportation (11).Optically thick atomic ensemble has been proved to be an ex-

cellent candidate for quantum memory (12–17), with promisingexperimental progress including the entanglement between twoatomic ensembles (18, 19), generation of nonclassical fields (12,13), efficient storage and retrieval of photonic qubits (14), sub-second storage time (17), and demonstration of a preliminaryquantum repeater node (15, 16). Quantum teleportation has beendemonstrated with single photons (20–22), from light to matter (23,24), and between single ions (25–27). However, quantum telepor-tation between remote atomic ensembles has not been realized yet.In this article, we report a teleportation experiment between two

atomic-ensemble quantum memories. The layout of our experi-ment is shown in Fig. 1. Two atomic ensembles of 87Rb are createdusing magnetoopticaltrap and locate at two separate nodes. Theradius of each ensemble is ∼1 mm. We aim to teleport a singlecollective atomic excitation (spin wave state) from ensemble A to

B, which are linked by a 150-m-long optical fiber and physicallyseparated by ∼0.6 m. The spin wave state can be created throughthe process of electromagnetically induced transparency (28) orweak Raman scattering (6), and can be written as follows:

��dir�= 1ffiffiffiffiN

pXj

eikdir · rj��g . . . sj . . . g�; [1]

where “dir” refers to the direction of the spin wave vector kdir, rjrefers to the coordinate of jth atom, and N refers to the numberof atoms. The atoms are in a collective excited state with onlyone atom excited to the state jsi and delocalized over the wholeensemble. The spin wave can be converted to a single photonwith a high efficiency (>70% has been reported in refs. 29 and30) due to the collective enhancement effect (6, 28).Our experiment starts with initializing the atomic ensemble A

in an arbitrary state to be teleported jψiA = αj↑iA + βj↓iA, where↑ (up) and ↓ (down) refer to the directions of the spin wavevector relative to the write direction in Fig. 1, and α and β arearbitrary complex numbers fulfilling jαj2 + jβj2 = 1. To do so, themethod of remote-state preparation (31) is used. By applying awrite pulse, we first create a pair of entanglement between thespin wave vector and the momentum (emission direction) of thewrite-out photon (photon 1 in Fig. 1) through Raman scattering(32). The momentum degree of the write-out photon is laterconverted to the polarization degree by a polarizing beam splitter(PBS). In this way, we create the entanglement between the spinwave state of the ensemble and the polarization of the write-outphoton. The created atom–photon entangled state can be writtenas jΨ−i1A = 1=

ffiffiffi2

p ðjHi1j↑iA − jV i1j↓iAÞ. Next, we perform a pro-jective measurement of photon 1 in the basis of jψi1=jψ⊥i1, wherejψi1 = αjHi1 + βjV i1 and jψ⊥i1 = β*jHi1 − α*jV i1. Due to theanticorrelation nature of jΨ−i in an arbitrary basis, if the mea-surement result gives jψ⊥i1, we can infer that the state of en-semble A will be projected to jψiA. Experimentally, we use acombination of a quarter-wave plate, a half-wave plate, and apolarizer to measure photon 1 in an arbitrary basis. Due to theprobabilistic character in the Raman scattering process, the exci-tation probability for each write pulse is made to be sufficiently low(∼0.003) to suppress the double-excitation probability. Therefore,the write process needs to be repeated many times to prepare theatomic state successfully. The storage lifetime for prepared states ismeasured to be 129 μs, which is mainly limited by motion induceddephasing (33). In our experiment, we select the following sixinitial states to prepare: j↑iA, j↓iA, j+iA, j−iA, jRiA and jLiA withj±iA = 1=

ffiffiffi2

p ðj↑iA ± j↓iAÞ and jR=LiA = 1=ffiffiffi2

p ðj↑iA ± ij↓iAÞ by

Author contributions: X.-H.B. and J.-W.P. designed research; X.-H.B., X.-F.X., C.-M.L., andZ.-S.Y. performed research; X.-H.B., X.-F.X., C.-Y.L., and J.-W.P. analyzed data; X.-H.B.,C.-Y.L., and J.-W.P. wrote the paper; and J.-W.P supervised the whole project.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

See Commentary on page 20169.1To whom correspondence may be addressed. E-mail: cylu@ustc.edu.cn or pan@ustc.edu.cn.

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projecting photon 1 into the corresponding states jψ⊥i1. To verifythis state preparation process, we map the prepared spin waveexcitation out to a single photon (photon 2 in Fig. 1) by applyinga read pulse on ensemble A and analyze its polarization using thequantum state tomography (34). The reconstructed six spin wavestates (ρi with i = 1–6) of ensemble A are plotted in the Blochsphere as shown in Fig. 2. The average fidelity between themeasured and ideal states is 97.5(2)%.Next, we establish the necessary quantum channel connecting

the two atomic ensembles. The channel is in the form of en-tanglement between the spin wave state of atomic ensemble B(stationary and storable) and the polarization of a single photon,which can be distributed far apart. In our experiment, it is cre-ated through the process of Raman scattering. Each time whena write pulse is applied, with a small probability, a pair ofentangled state between the scattered photon 3 and the spinwave of ensemble B is generated in the following form:

��Φ+�3B = 1=

ffiffiffi2

p �jHi3��↑�B +

��V�3

��↓�B�: [2]

To test the robustness of our teleportation protocol over longdistance, we send photon 3 to node A through a 150-m-longsingle-mode fiber that has an intrinsic loss of about 11:4%. Thetemperature-dependent slow drift of polarization rotationcaused by this fiber is actively checked and compensated.To teleport the state jψiA from node A to B, we need to make

a joint Bell state measurement (BSM) between jψiA and photon

3. It is, however, difficult to perform a direct BSM between asingle photon and a spin wave. To remedy this problem, weconvert the spin wave excitation in atomic ensemble A to a singlephoton (photon 2) by shining a strong read pulse. Before theconversion, to compensate the time delay of entanglement prepa-ration in node B and transmission of photon 3 from node B to nodeA, the prepared state jψiA is stored for 1.6 μs. The photons 2 and 3are then superposed on a PBS for BSM (see the setup in Fig. 1).Stable synchronization of these two independent narrow-bandsingle photons that have coherence length of ∼7.5 m is much easiercompared with previous photonic teleportation experiments withparametric down-conversion where the coherence length of thephotons is a few hundred micrometers (20), and thus extendable toa large-scale implementation. In addition to ensuring a good spatialand temporal overlap between photons 2 and 3, their frequencyshould also be made indistinguishable. Thus, the jgi and jsi in the Λlevel schemes are arranged to be opposite between A and B, asshown in Fig. 1 as insets. The initial state where the atoms stay isalso opposite. By coincidence detection and analysis of the twooutput photon polarization in the j±i basis (35), we are able todiscriminate two of them, i.e., jΦ+i23 and jΦ−i23. The classicalmeasurement results are sent to node B. When we detect jΦ+i23,the teleportation is successful without further operation, whereas incase of jΦ−i23, a π phase shift operation on j↓iB is required.To evaluate the performance of the teleportation process, the

teleported state in atomic ensemble B is measured by applyinga read laser converting the spin wave excitation to a single

A B

Fig. 1. The experimental setup for quantum teleportation between two remote atomic ensembles. All of the atoms are first prepared at the ground state jgi.The spin wave state of atomic ensemble A is prepared through the repeated write process. Within each write trail, with a small probability, entanglementbetween the spin wave vector and the momentum of the write-out photon is created. A polarizing beam splitter (PBS) converts the photon’s momentum to itspolarization. A click in D1 heralds a successful state preparation for ensemble A. Conditioned on a successful preparation, a write pulse is applied on atomicensemble B, creating a pair of photon–spin wave entanglement jΦ+i3B. The scattered photon 3 travels through a 150-m-long single-mode fiber and subjects toa Bell state measurement together with the read-out photon 2 from the atomic ensemble A. A coincidence count between detector D2 and D3 heralds thesuccess of teleportation. To verify the teleported state in atomic ensemble B, we convert the spin wave state to the polarization state of photon 4 by applyingthe read pulse. Photon 4 is measured in arbitrary basis with the utilization of a quarter-wave plate (QWP), a half-wave plate (HWP), and a PBS. The leakage ofthe write and read pulse into the single-photon channels are filtered out using the pumping vapor cells (PVC). The Λ -type level schemes used for bothensembles are shown in the Insets.

20348 | www.pnas.org/cgi/doi/10.1073/pnas.1207329109 Bao et al.

photon (photon 4 in Fig. 1) whose polarization is analyzed.Quantum state tomography for the teleported state is applied forall of the six input states shown in Fig. 2. For the events in whichBSM result is jΦ−i, an artificial π phase shift operation is appliedto the reconstructed states. Based on this result, we calculate thefidelities between the prepared input states and the teleportedstates. Because in this case both the input and teleported statesare mixed states in practice, we adopt the equation (36) ofFðρ1; ρ2Þ≡ ftr½ð ffiffiffiffiffi

ρ1p

ρ2ffiffiffiffiffiρ1

p Þ1=2�g2, where ρ1 and ρ2 are arbitrarydensity matrices. Calculated results are listed in Table 1. Weobtain an average fidelity of Favg = 95± 1%, which is well abovethe threshold of two-thirds attainable with classical means (37).Furthermore, the state tomography results allow us to charac-terize the teleportation process using the technique of quantumprocess tomography (38). An arbitrary single-qubit operation onan input state ρin can be described by a process matrix χ, whichis defined as ρ=

P3i;j=0χij bσiρinbσj, where ρ is the output state and

bσi are Pauli matrices with bσ0 = I, bσ1 = bσx, bσ2 = bσy, and bσ3 = bσz. Weuse the maximum-likelihood method (38) to determine themost likely physical process matrix of our teleportation process.The measured process matrix is shown in Fig. 3. For an idealteleportation process, there is only one nonzero element ofχideal00 = 1. Therefore, we get the calculated process fidelity ofFproc ≡ trðχχidealÞ= 87ð2Þ% with the error calculated based on the

Poisson distribution of original counts. The deviation from unitfidelity is mainly caused by the nonperfect entanglement ofjΦ+i3B and nonperfect interference on the PBS in the BSM stage.We note that, in our experiment, the auxiliary entanglement

pair between atomic ensemble B and photon 3 is probabilistic;thus, our teleportation process also works probabilistically. Foreach input state, our teleportation process succeeds with aprobability of ηAPB=2 ’ 10−4, where ηA (7%) is the detectedretrieval efficiency of ensemble A, PB (3× 10−3) is the detectionprobability of a write-out photon from ensemble B during eachwrite trial, and the one-half is due to the efficiency of BSM (twoBell states of four). The success probability is 4 orders ofmagnitude larger than the previous trapped-ion teleportationexperiment (27). Another useful feature of our experiment isthat a trigger signal is available to herald the success of tele-portation, which can benefit many applications including long-distance quantum communication (6, 9) and distributed quan-tum computing (7, 39). This trigger signal comes from the co-incidence detection between D2 and D3 in the BSM stage. Let usfurther analyze the read-out noise of ensemble A and high-or-der excitations of ensemble B. We find that the BSM signal ismixed with some noise, which could give a fake trigger forteleportation. There are mainly three contributions for the BSMsignal as listed below:

from A&B A Bprobability ηAPB ηAPA P2

B; [3]

where PA is the detection probabilities of a write-out photonfrom ensemble A during each write trial. The first term is thedesired term, which corresponds to the case that one photon isretrieved out from node A and the other is the write-out photonfrom node B. The second term means that both photons arefrom node A, with one being the retrieved photon and the otherthe read-out noise photon, which has a similar probability as theexcitation probability. The third term comes from the case thatboth photons are from node B caused by double excitations. Tohave a high heralding fidelity, the proportion of the first termshould be as high as possible, i.e., the following requirementshould be fulfilled:

PA � PB � ηA: [4]

In our experiment PB � ηA is satisfied (3× 10−3 � 7%). Tofulfill the first half inequality of Eq. 4, we reduce the excitationprobability of ensemble A to PA ’ 0:30× 10−3. Under thiscondition, we remeasure the teleported states for the six inputsand obtain an average postselected fidelity of Favg = 93ð2Þ%.

Fig. 2. Bloch sphere representation of the tomography result for the pre-pared atomic states. The solid arrow lines represent six target states (j↑i, j↓i,j+i, j−i, jRi, and jLi). The dashed arrow lines correspond to the six measuredstates (ρi with i = 1–6). Calculated fidelities between the measured andtarget states are shown, showing a near-perfect agreement between thetwo states. Errors for the fidelities are calculated based on the Poisson sta-tistics of raw photon counts.

Table 1. Calculated fidelities between the prepared states ofatomic ensemble A and the teleported states in atomic ensembleB based on the quantum state tomography results using themaximum-likelihood method

Input state of ensemble A Fidelity, %

ρ1 97(1)ρ2 93(2)ρ3 96(2)ρ4 94(3)ρ5 97(4)ρ6 96(2)

A B

Fig. 3. Measured process matrix χ for the teleportation. The real part isshown in A, and the imaginary part is shown in B. For an ideal teleportationprocess, there should be only one nonzero element (χ00 = 1).

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This fidelity is slightly lower than the high excitation case (Table1) due to the relatively higher contribution of background noise,which mainly includes leakage of control laser (write, read, filtercell pumping beam, etc.), stray light, and detector dark counts.The fidelity of heralded teleportation, defined as Fher ≡ Fηherwith the heralding efficiency ηher ≡ p234=p23ηB in which p234 andp23 are the joint detection probabilities of corresponding detectorsconditioned on a detection event on D1, is measured to be88ð7Þ% averaged over the six different input and output states.The imperfection of this heralding fidelity is mainly limited bythe high-order excitations and background excitations. High-or-der excitations can be inhibited by making use of the Rydbergblockade effect (40, 41). Background excitations can be sup-pressed by putting the atomic ensemble inside an optical cavityso that the emission of scattered photons is enhanced only inpredefined directions (29). These methods can in principle boostthe heralding efficiency without lowering the excitation proba-bility of ensemble A.In summary, we have experimentally demonstrated heralded,

high-fidelity quantum teleportation between two atomic ensem-bles linked by a 150-m-long optical fiber using narrow-band singlephotons as quantum messengers. From a fundamental point ofview (42), this is interesting as a teleportation between two mac-roscopic-sized objects (18) at a distance of macroscopic scale.From a practical perspective, the combined techniques demon-strated here, including the heralded state preparation with feed-back control, coherent mapping between matter and light, andquantum state teleportation, may provide a useful tool kit forquantum information transfer among different nodes in a quan-tum network (7–9). Moreover, these techniques could also beuseful in the scheme for measurement-based quantum computingwith atomic ensemble (39), e.g., to construct and connect atomiccluster states. Compared with the previous implementation withtrapped ions (27), for each input state, our experiment featuresa much higher (4 orders of magnitude) success probability. This isan advantage of the atomic ensembles where the collective en-hancement enables efficient conversion of atomic qubits to pho-tons in specific modes, avoiding the low efficiencies associatedwith the free space emission into the full solid angle in case ofsingle ions (27). Methods for further increasing the successprobability include using a low-finesse optical cavity to improve

the spin wave-to-photon conversion efficiency (29) (higher ηA),and using the measurement-based scheme and another assistedensemble to create the auxiliary photon–spin wave entanglementnear deterministically (higher PB) (15, 16). In the present ex-periment, the storage lifetime (∼129 μs) of the prepared spinwave states in the quantummemories slightly exceeds the averagetime required (∼97.5 μs) to create a pair of assistant remote en-tanglement for teleportation. The storage lifetime in the atomicensembles can be increased up to 100 ms by making use of opticallattices to confine atomic motion (17). With these improvements,we could envision quantum teleportation experiments amongmultiple atomic-ensemble nodes in the future.

MethodsOur experiment is operated with a repetition rate of 71.4 Hz. Within eachcycle, the starting 11 ms is used to capture the atoms and cool them to ∼100μK. The following 3-ms duration is used for the teleportation experiment,during which the trapping beams and the magnetic quadrupole field areswitched off. Optical pumping to the Zeeman sublevel ofmF = 0 is applied forensemble A to increase the storage lifetime. Each write trial for ensemble Aand B lasts for 3.38 μs and 975 ns, respectively. The probability to create a pairof photon–spin wave entanglement in node B within each write trial is about0.01; thus, the average time required to create a pair of assistant entangle-ment for teleportation is about 97.5 μs. The write/read control pulses havea time duration of 50 ns, a beam waist of ∼240 μm. The write/read beams forboth ensembles are on resonance with the corresponding transitions shownin Fig. 1. The polarization for the write (read) beams is vertical (horizontal),that is, perpendicular (in parallel) to the drawing plane in Fig. 1. The Rabifrequency for the write and read beams is 1.7 and 14.6 MHz, respectively. Thedetection beam waist for the write-out and read-out single photons is ∼100μm. The intersection angle between the write beam and the write-out pho-ton mode for ensemble A(B) is 0.5°(3°). All of the control pulse sequences aregenerated from a FPGA logic box. The output from single-photon detectors(D1 to D4) are either registered with a multichannel time analyzer during thesetup optimization, or with the logic box during data measurement for theteleportation process.

ACKNOWLEDGMENTS. This work was supported by the National NaturalScience Foundation of China, National Fundamental Research Program ofChina Grant 2011CB921300, the Chinese Academy of Sciences, the YouthQianren Program, the European Commission through a European ResearchCouncil (ERC) Grant, and the Specific Targeted Research Projects (STREP)project Hybrid Information Processing (HIP).

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